The computerized tomography (CT) technology has been widely used for the medical diagnosis and the industrial non-destructive inspection. In various CT systems, the mostly-used ones are fan-beam or cone-beam X-CT systems. The existing X-CT scan systems adopt a circular orbit scan mode and a linear array detector (corresponding to the fan-beam X-CT) or a planar array detector (corresponding to the cone-beam X-CT) because the circular orbit scan mode only requires a simple and easy implemented mechanical structure, and the corresponding reconstruction algorithm has been developed and is reliable. Furthermore, the detectors are placed symmetrically with respect to the connecting line from the X-ray source to the rotation axis or slightly deviated in the case of detector slightly-moving technique. Particularly, the circular orbit scan mode based X-CT system plays an important role in the industrial non-destructive inspection hitherto.
Among the circular orbit cone-beam or fan-beam CT reconstruction algorithms, the filtered-backprojection (FBP) algorithm is widely used, which has several advantages such as simple mathematical equation, quick computation, easy implementation and so on. The famous FDK algorithm, for example, is a FBP algorithm. However, the conventional FBP algorithm requires the projection data can not be truncated in the detector direction, which means that the detector must be long enough in the transverse direction to cover the entire cross section of the object. Therefore, when the object under measure has a large volume, the X-ray beams need to have a large spread angle and the detector needs to be large in size to completely cover the object. These requirements are hard to meet in some applications.
When a large cross section object is to be measured, one practical method is to use the second generation scan mode, rotation plus shift. In particularly, the entire object is covered through several scans firstly, and then the whole projection data is obtained by means of a rebinning method. However, the scan mode is long in time and costs much effort, which largely adds the hardware complexity and overhead of the system, and the data amount is doubled and the computation is also increased, thus the reconstruction speed is lowed.
According to the CT scan principle and the reconstruction theory, in the case of circular orbit scan, reconstructing mathematically the whole object does not need all the projection data which covers the whole object in 360 degrees. In principle, the projection data is redundant by half, that is to say, half of the projection data is redundant. Therefore, only half of the projection data is needed to accurately reconstruct the whole object tomographic images.